Problem: Ben is $12$ years older than Ishaan. Ben and Ishaan first met two years ago. Three years ago, Ben was $4$ times as old as Ishaan. How old is Ben now?
Solution: We can use the given information to write down two equations that describe the ages of Ben and Ishaan. Let Ben's current age be $b$ and Ishaan's current age be $i$. The information in the first sentence can be expressed in the following equation: ${b = i + 12}$ Three years ago, Ben was $b - 3$ years old, and Ishaan was $i - 3$ years old. The information in the third sentence can be expressed in the following equation: ${b - 3 = 4(i - 3)}$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$, it might be easiest to solve our first equation for $i$ and substitute it into our second equation. Solving our first equation for $i$, we get: ${i = b - 12}$. Substituting this into our second equation, we get the equation: ${b - 3 = 4(} {(b - 12)}{ - 3)}$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 3 = 4b - 60$. Solving for $b$, we get: $3 b = 57$. $b = 19$.